Pre- and post-selected quantum states: density matrices, tomography, and Kraus operators

TL;DR

This paper develops a formalism for describing and characterizing two-time quantum states, including a tomography method and insights into the role of Kraus operators, advancing understanding of pre- and post-selected quantum systems.

Contribution

It introduces a density vector formalism for 2-time states, provides a tomography method for unknown states, and links measurements on 2-time states to bipartite states.

Findings

A general 2-time state is characterized by a measurement-independent density vector.

The tomography method cannot be realized by weak or projective measurements.

Any measurement on a 2-time state can be mapped to a measurement on a bipartite state.

Abstract

We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed between the preparation and post-selection. We provide a method for performing tomography of an unknown 2-time density vector. This procedure, which cannot be implemented by weak or projective measurements, brings new insight to the fundamental role played by Kraus operators in quantum measurements. Finally, after showing that general states and measurements are isomorphic, we show that any measurement on a 2-time state can be mapped to a measurement on a preselected bipartite state.